An approximation for reflectance from semi-infinite medium
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An approximation for the reflectance from a semi-infinite medium

I introduce a simple analytical approximation for the reflectance from a semi-infinite medium which has scattering and absorption. Its inverse transformation (reflectance to scattering/absorption coefficients) has also simple analytical solution.

See build/transfer.pdf (currently written only in Japanese).

Although this work is original, it is obvious that similar works exist (…​and they are most likely better than mine) since it seems a very basic and common problem. Unfortunately I cannot find them, at least freely avaiable on the Web. Let me know if you find them and I should cite them.

TL; DR

ks : Scattering coefficient
ka : Absorption coefficient
 k : Attenuation (= ks + ka)
 R : Reflectance
 γ = 1.4

ks, ka => R
    P = sqrt(ka / (ks + ka))
    R = (1 - P) / (1 + γ * P)

R, k => ks, ka
    ka = k * ((1 - R) / (1 + γ * R)) ^ 2
    ks = 1 - ka